Collective modes in relativistic npe matter at finite temperature

Isospin and density waves in neutral neutron-proton-electron (npe) matter are studied within a relativistic mean-field hadron model at finite temperature with the inclusion of the electromagnetic field. The dispersion relation is calculated and the collective modes are obtained. The unstable modes are discussed and the spinodals, which separate the stable from the unstable regions, are shown for different values of the momentum transfer at various temperatures. The critical temperatures are compared with the ones obtained in a system without electrons. The largest critical temperature, 12.39 MeV, occurs for a proton fraction y_p=0.47. For y_p=0.3 we get $T_{cr}$ =5 MeV and for y_p>0.495 $T_cr\lesssim 8$ MeV. It is shown that at finite temperature the distillation effect in asymmetric matter is not so efficient and that electron effects are particularly important for small momentum transfers.